Is there branching logic, i.e. do you skip certain questions based on the
answers to earlier questions?

I did have some branchings, but I ended up removing them. I do have some page
separators.

Does anybody have any inputs? Currently I have a total  of 73 responses, but only
39 replies are shown, 32 are missing  based on the skipped replies and 2 are
missing. Is there a way for me to look into the database to see the responses?
We're getting ready to do some analyses of the responses  but can't do this until
I find  out where the other responses are.

To be honest there is not enough details to help you.

1.) Did you require all questions to have an answer
2.) How did you create the survey?
3.) did you remove the logic before or after the survey  went live?

1) None of the questions are required.
2) The survey  was created  from a survey template (saved as a template from an
old survey).
3) I removed the logic before the survey went live.

Additional info:
4) All users can view and only edit their own survey.
5) Since my last email, the total  is now 74, but still only 39 responses  and 32
missing. The most recent response is not visible. And there is no pattern
between the skipped responses.

Are there any limiting criteria in either of the two views you mentioned?

I don't see where I can modify the views.

Here is another odd thing, I noticed some higher # responses  have an earlier
modified date and time than the lower # responses. For example: Response
#23Â was modified on 1/9/10 13:00 and Response #22 was modified on 1/9/10 14:00.
How is this possible?

This is a common issue with multi-page surveys. I forget the exact terminology
in the UI but users can save their response in draft so it remains checked out
to them. As with all SharePoint items that are newly created  and checked out,
the item is visible only to the creating user. Even site  collection admins can't
see it.

If you look on the web, people have found the draft responses  using database
queries, but that is (of course) unsupported. You may have to follow up with the
user population asking them to make sure they finalise their responses.

It helps if you can tie their completed response to some aspect of their
compensation.

We were able to query the database and saw the results. But does anybody know
what tp_version=1 means? We were able to figure out tp_version=3 means
completed, tp_version=2 means saved and tp_version=5 means deleted. Now we just
don't know what tp_version=1 means.

This is a known issue that I would discussing where site  administrators and users are unable to view responses  of an incomplete survey  in Sharepoint. When you use Page Separator type questions in a survey, the respondents get an option to type or choose their response and move to the next question or Save survey so that it can be completed at a later time. When investigating we found that the incomplete post is only and only visible to that respondent who added his/her response partially. The site administrators and other users are unable to view the response. However, the number  of Responses shows  the updated number but in no way we can check that incomplete response other than that respondant. We have tried toggling and switching the web part views but to no avail. We found that this is supposed to be an intended design of the product which we can expect to change in the next release or so but there is no such updates from the confirmed sources.

Alternative: The survey creator can either choose not to have a Page Separator type question in the survey or use a workaround as per the blog mentioned below where the survey creator can hide the Save button and can still the Page Separator type questions in the survey. In this way the respondents will not get an option to save the survey and will need to complete the same. This should populate the responses correctly as per the total  number of responses in the survey.

Here is the link to the workaround: http://www.endusersharepoint.com/?p=1371